{"title":"The polynomial equation XR + QY = Φ: A characterization of solutions","authors":"E. Emre, L. Silverman","doi":"10.1109/CDC.1980.271845","DOIUrl":null,"url":null,"abstract":"We consider the solutions of the equation XR + QY + Φ. Here Q, R, Φ are given p x q, m x t and p x t polynomial matrices over a field k. X and Y are p x m and q x t polynomial matrices which are unknown. Using certain recent results on the realization of matrix fraction descriptions of transfer matrices, we give a characterization (parameterization) of all possible (X, Y) which solve this equation. This also provides a system theoretic interpretation for this equation.","PeriodicalId":332964,"journal":{"name":"1980 19th IEEE Conference on Decision and Control including the Symposium on Adaptive Processes","volume":"83 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"1980-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"1980 19th IEEE Conference on Decision and Control including the Symposium on Adaptive Processes","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1109/CDC.1980.271845","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 0
Abstract
We consider the solutions of the equation XR + QY + Φ. Here Q, R, Φ are given p x q, m x t and p x t polynomial matrices over a field k. X and Y are p x m and q x t polynomial matrices which are unknown. Using certain recent results on the realization of matrix fraction descriptions of transfer matrices, we give a characterization (parameterization) of all possible (X, Y) which solve this equation. This also provides a system theoretic interpretation for this equation.
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